purpose and outcomes -...

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Day 1: Addition and Subtraction

MATHEMATICS ACHIEVEMENT ACADEMY, GRADE 2

• What is the purpose of the mathematics academies?

• What are the outcomes of the mathematics academies?

Purpose and Outcomes

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Texas Gatewayhttp://www.texasgateway.org/

• Mathematics TEKS: Supporting Information

• Vertical Alignment Charts

Materials

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1

2

Rotating Trios

• Be fully present.

• Minimize distractions.

• Minimize “air time.”

• Take a chance.

• Celebrate accomplishments.

Participation Norms

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• Listen.

• Be involved.

• Contribute ideas.

• Participate by asking questions.

• Develop understanding, if not at the beginning, by the end.

Krusi, 2009

Discourse Norms

• Look for patterns in order to make generalizations.

• Make connections among models, representations, and algorithms.

• Communicate using academic vocabulary. • Use mistakes as opportunities to support new

learnings about mathematics.

Yackel & Cobb, 1996

Mathematics Norms

Learning Progression

A learning progression is a sequenced set of subskills and bodies of enabling knowledge that, it is believed, students must master en route to mastering a more remote curricular aim.

In other words, it is composed of step-by-step building blocks students are presumed to need in order to successfully attain a more distant, designated instructional outcome.

Popham, 2008

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• Create a graphic organizer to show a learning progression from kindergarten to fourth grade for the concepts of addition and subtraction.

• Trade your poster with another table group.

o How are the big ideas of the other group’s poster similar to your group’s poster?

o How are they different?


Where would you place the grade-level student expectations on your graphic organizer?



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How can a learning progression support planning for focused, targeted, and systematic instruction?


• 2(4)(C) The student is expected to solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms.

• 2(7)(C) The student is expected to represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem.

Whole Number Addition and Subtraction

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Balanced Pre-Assessment

The Role of Pre-Assessment

Where do we start with this year’s students?

What gaps do my students have?

Which adjustments are needed for the whole group?

Which adjustments are needed for a small group?

MSTAR Math Academy, 2010

Target Knowledge and

Skills

Foundational Knowledge and

Skills

Bridging Knowledge and Skills

Connections Across the Knowledge Representations

Balanced Pre-Assessment

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• What are the broad and deep ideas that students must master to be successful in grade 2 mathematics?

• What are the concepts and procedures from grade 1 that students must have mastered?

• What are the foundational knowledge and skills that students may use to build towards mastery?


Target Knowledge and Skills

Foundational Knowledge and Skills

Bridging Knowledge and Skills• What are the bridging knowledge

and skills that students may use to connect foundational understandings to target understandings?

• What are the target knowledge and skills mathematics that students must master?

Guiding Questions for Balanced Pre-Assessment

Guiding Questions for Examining Student Work

Models of Mathematics• What models do we see students using the most often?• With what models are students most successful?• What models are we not seeing students use?• With what models are students least successful?

Mathematical Processes and Procedures• What processes or procedures are students

using the most often?• With what processes or procedures are

students most successful?• What misconceptions are present in this work?• What steps are students taking most often?

Sorting Student Work

Where do we build from?

What do we need to develop?

What gaps do we need to address?


Target Knowledge and Skills

Foundational Knowledge and Skills

Bridging Knowledge and Skills

Connections Across Knowledge and Representations

Instructional Decisions

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Where do we build from?

What do we need to develop?

What gaps do we need to address?

Whole Class

Small Group

Pre-Assessment Instructional Decisions

Best Practices: Guiding Questions for BalancedPre-Assessment and Examining Student Work

1. Determining Sums Using Mental Strategies2. Determining Differences Using Mental Strategies3. Compensation with Addition4. Compensation with Subtraction5. Compatible Numbers and Making Tens

Computation of Addition and Subtraction

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1. Determining Sums Using Mental Strategies2. Determining Differences Using Mental Strategies3. Compensation with Addition4. Compensation with Subtraction5. Compatible Numbers and Making Ten6. Solving Addition Problems Using Mental Strategies7. Solving Subtraction Problems Using Mental Strategies


2(4)(B) The student is expected to add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations.


Whole Number Addition and Subtraction Based on Place Value and Algorithms

1. Determining Sums Using Mental Strategies2. Determining Differences Using Mental Strategies3. Compensation with Addition4. Compensation with Subtraction5. Compatible Numbers and Making Tens

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1. Determining Sums Using Mental Strategies2. Determining Differences Using Mental Strategies

• Decomposing numbers and using expanded form

• Using place value knowledge and allowing students to think about joining or separating tens and joining or separating ones


3. Compensation with Addition4. Compensation with Subtraction

• The relative position on a number line – shifting numbers on a number lineNumbers are chosen to allow the use of compatible numbers for an equivalent expression.

• The preservation of a number• The visual distance between numbers


5. Compatible Numbers and Making Tens

• Making tens or multiples of ten

• Building on students prior knowledge of combining tens and building on understanding of place value


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1. Determining Sums Using Mental Strategies2. Determining Differences Using Mental Strategies3. Compensation with Addition4. Compensation with Subtraction5. Compatible Numbers and Making Tens6. Solving Addition Problems Using Mental Strategies7. Solving Subtraction Problems Using Mental Strategies


Using Anchor Charts

Using Anchor Charts

Anchor Charts:Created with students as a summary of learning

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• Why is it important for an anchor chart to be developed by the class rather than presented to the class?

• How and when might students refer to an anchor chart?

Using Anchor Charts

Check Point: Computation of Addition and Subtraction

Debriefing Mental Strategies

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32 47 3247

79

30 40 2 7

70 9

79

How does the use of mental strategies connect to the standard algorithm?


96 45 9645

51

90 40 6 5

50 151



32 4930 40 2 9

70 1170 1110

8

0

1

1

80 1

13249

81



14

100 38

100 30 8

100 0 0 30 0 8


10038



0 10010

100 38

100 30 8

100 0 0 30 0

0 300

8

0 0 8

100

1 0 038



1090

10 00

100 38

100 30 8

100 0 0 30 0 8

100 0 00 30 8

910 10 0

01 03 8


15


910 100

1 0

2

03 86

900 100 10

100 38

100 30 8

100 0 0 30 0 8

100 0 0 30 0 8

60 262



(100 1)(38 1)

993762

910 100

1 0 03 8

6 2


1. Representation Card Match2. Fruit Stand3. Representations for Addition and Subtraction 4. Ice Cream Purchases

Represent and Solve One-step Problems

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1. Representation Card Match2. Fruit Stand3. Representations for Addition and Subtraction 4. Ice Cream Purchases

Represent and Solve One-step Problems

1. Ice Cream Purchases2. Fruit Stand3. Representation Card Match4. Representations for Addition and Subtraction

Possible Sequence of Activities

Check Point: Represent and Solve Problems

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All students must use the same model.

Agree or Disagree?

Students should choose the model that makes most sense.

Agree or Disagree?

All models work for all problems.

Agree or Disagree?

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Solve One-Step Problems

Solve One-Step Problems: Carousel

• How are the two solution strategies similar?• How are they different?

Make notes on the poster to indicate similarities and differences.

• If you were asked to solve this problem, would your solution strategy look like one on the poster, or do you have thoughts about a third way to solve this problem?

Solve One-Step Problems: Carousel

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Solve One-Step Problems: Speed Learning

• What representations did you find yourself using? Why?

• What mental strategies did you find yourself using? Why?

Solve One-Step Problems: Speed Learning

Solve One-Step Problems

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• Be fully present.

• Minimize distractions.

• Minimize “air time.”

• Take a chance.

• Celebrate accomplishments.

Participation Norms

• Listen.

• Be involved.

• Contribute ideas.

• Participate by asking questions.

• Develop understanding, if not at the beginning, by the end.

Krusi, 2009

Discourse Norms

• Look for patterns in order to make generalizations.

• Make connections among models, representations, and algorithms.

• Communicate using academic vocabulary.

• Use mistakes as opportunities to support new learning about mathematics.

Mathematics Norms

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AlgorithmAnchor ChartBalanced Pre-AssessmentFoundational–Bridging–Target Knowledge and SkillsLearning ProgressionRepresent

Equations Number Lines Pictorial Models

Strategies/Mental Strategies/Solution Strategies Place Value Properties of Operations Relationship Between Addition and Subtraction

Academic Vocabulary

Learning ProgressionWhole Number Addition

and SubtractionDiverse Learners

What confirming/new ideas did you hear today?

How can you move new and intriguing ideas to action?

Exit Slip

purpose and outcomes -...

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